Author: Raquel Dourado Coutinho, Marcos dos Santos
Date: 2021-01-30

# AHP-TOPSIS-2N Example

#### Raquel Dourado Coutinho, Marcos dos Santos

#### 2021-01-30

## Introduction

##### Multicriteria Decision Analysis (MCDA) and the AHP-TOPSIS-2N method.

The objective of MCDA is to assist in decisions with multiple criteria. Multicriteria methods can be useful in several problems in business and even in personal life. AHP-TOPSIS-2N is a hybrid method build from the AHP (Analytic Hierarchy Process) and TOPSIS-2N (Technique for Order of Preference by Similarity to Ideal Solution - with two normalizations).

AHP-TOPSIS-2N uses the AHP to calculate the criteria weights and uses TOPSIS twice to generate rankings, each time with a different kind of normalization. This can allow the comparison of results and the analysis of the robustness. A consistency ratio is calculated, and when it is higher than 10%, it is required to check judgments on criteria comparison.

## Example

As an example, this vignette uses a case of row material supplier evaluation. The goal is to choose among A, B, and C suppliers based on the product cost, product quality (1 to 5), and the lead time. Below we have the decision matrix (alternatives x criteria).

Alternatives | Cost | Quality | Lead Time
--- | --- | --- | ---
A1 | 1100 | 5 | 25
A2 | 850 | 3.5 | 10
A3 | 950 | 4 | 30

After defining the decision matrix, it’s time to define a matrix with a pairwise comparison of the criteria, using the Saaty scale (1-9).

| Cost | Quality | Lead Time
--- | --- | --- | ---
Cost | 1 | 1 | 3
Quality | 1 | 1 | 5
Lead Time | 1/3 | 1/5 | 1

The criteria comparison matrix can be read like this: “Cost is so important as Quality, Cost has moderate importance over Lead Time, Quality has strong importance over Lead Time.”

    library(ahptopsis2n)

    # define the decision matrix
    decision<-matrix(c(1100, 5, 25,
                       850, 3.5, 10,
                       950, 4, 30), ncol=3, byrow=TRUE)

    rownames(decision)<- c("A1", "A2", "A3")

    #define criteria matrix with pairwise comparison
    criteria<-matrix(c(1, 1, 3,
                       1, 1, 5,
                       1/3, 1/5, 1), ncol=3, byrow=TRUE)

    # define each criterion objective
    minmax<-c("min", "max", "min")

    # associate the objects to the function arguments and run the function
    ahptopsis2n(decision=decision, criteria=criteria, minmax=minmax)
    #> [[1]]
    #>            [,1]
    #> [1,] 0.02505497
    #>
    #> [[2]]
    #>       values ranking
    #> A1 0.5754562       1
    #> A2 0.4553086       2
    #> A3 0.3517222       3
    #>
    #> [[3]]
    #>       values ranking
    #> A1 0.5374991       1
    #> A2 0.4669885       2
    #> A3 0.4359941       3

As we can see, the result is a list with a consistency ratio and two data frames with priority sorting of the alternatives.

### References

De Souza, L. P., Gomes, C. F. S. and De Barros, A. P. (2018). Implementation of New Hybrid AHP–TOPSIS-2N Method in Sorting and Prioritizing of an it CAPEX Project Portfolio. International Journal of Information Technology & Decision Making. DOI: 10.1142/S0219622018500207.

Saaty, T.L. The Analytic Hierarchy Process. McGraw-Hill, New York. (1980)